Officers are investigating claims Toffees captain Phil Neville was spat on and punched by Liverpool fans as he prepared to take a throw-in.
They are also looking at reports that Reds skipper Steven Gerrard was subjected to hate-filled chants about his daughter.
As Neville, whose brother Gary still plays for United, prepared to take a throw supporters could be seen just inches away screaming down his neck.
And Gerrard faced a torrent of abuse as he walked to take a corner in front of visiting fans in the second half.
"Police will be speaking to the clubs involved today," said a spokesman for Merseyside Police.
Dave Lewis, the force's football liaison officer, who travels abroad with the teams when they play in Europe, will conduct the discussions.
Everton spokesman Ian Ross said: "We felt it necessary to try to involve the safety officers and police because we cannot have a situation where supporters are having physical contact with professional footballers during the game.
"We want to make sure that doesn't happen again at the Merseyside derby or any other game."